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Books on the topic 'Invariant properties'

Author: Grafiati

Published: 5 June 2025

Last updated: 1 August 2025

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1

Shu, Lin. On linear structure and phase rotation invariant properties of block 2[superscript l]-PSK modulation codes. National Aeronautics and Space Administration, 1990.

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2

Hall, Robert Ernest. Invariance properties of Solow's productivity residual. National Bureau of Economic Research, 1989.

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3

Barʹi͡akhtar, Viktor Grigorʹevich. Theory of adiabatic potential and atomic properties of simple metals. Gordon and Breach Science Publishers, 1999.

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4

Li, Weiping, and Shihshu Walter Wei. Geometry and topology of submanifolds and currents: 2013 Midwest Geometry Conference, October 19, 2013, Oklahoma State University, Stillwater, Oklahoma : 2012 Midwest Geometry Conference, May 12-13, 2012, University of Oklahoma, Norman, Oklahoma. American Mathematical Society, 2015.

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5

Koch, Anne. Determining Input-Output Properties of Linear Time-invariant Systems from Data. Logos Verlag Berlin, 2022.

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6

Sorrentino, Alfonso. Action-Minimizing Invariant Measures for Tonelli Lagrangians. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691164502.003.0003.

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This chapter discusses the notion of action-minimizing measures, recalling the needed measure–theoretical material. In particular, this allows the definition of a first family of invariant sets, the so-called Mather sets. It discusses their main dynamical and symplectic properties, and introduces the minimal average actions, sometimes called Mather's α‎- and β‎-functions. A thorough discussion of their properties (differentiability, strict convexity or lack thereof) is provided and related to the dynamical and structural properties of the Mather sets. The chapter also describes these concepts

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7

Children's naming of subject categories: Developmental differences in the invariant properties of category labelling. University Microfilms International, 1994.

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8

Sorrentino, Alfonso. From KAM Theory to Aubry-Mather Theory. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691164502.003.0002.

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This chapter discusses an illustrative example, namely the properties of invariant probability measures and orbits on KAM tori (or more generally, on invariant Lagrangian graphs). This will prepare the ground for understanding the main ideas and techniques that will be developed in the following chapters, without several technicalities that might be confusing to a neophyte.

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9

Iliopoulos, John. A Problem of Mass. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198805175.003.0004.

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This chapter examines the constraints coming from the symmetry properties of the fundamental interactions on the possible values of the masses of elementary particles. We first establish a relation between the range of an interaction and the mass of the particle which mediates it. This relation implies, in particular, that long-range interactions are mediated by massless particles. Then we argue that gauge invariant interactions are long ranged and, therefore, the associated gauge particles must have zero mass. Second, we look at the properties of the constituents of matter, the quarks and the

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10

Sorrentino, Alfonso. Action-Minimizing Curves for Tonelli Lagrangians. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691164502.003.0004.

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This chapter discusses the notion of action-minimizing orbits. In particular, it defines the other two families of invariant sets, the so-called Aubry and Mañé sets. It explains their main dynamical and symplectic properties, comparing them with the results obtained in the preceding chapter for the Mather sets. The relation between these new invariant sets and the Mather sets is described. As a by-product, the chapter introduces the Mañé's potential, Peierls' barrier, and Mañé's critical value. It discusses their properties thoroughly. In particular, it highlights how this critical value is re

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11

Azzouni, Jody. Attributing Knowledge. Oxford University Press, 2020. http://dx.doi.org/10.1093/oso/9780197508817.001.0001.

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The word “know” is revealed as vague, applicable to fallible agents, factive, and criterion-transcendent. It is invariant in its meaning across contexts and invariant relative to different agents. Only purely epistemic properties affect its correct application—not the interests of agents or those who attribute the word to agents. These properties enable “know” to be applied correctly—as it routinely is—to cognitive agents ranging from sophisticated human knowers, who engage in substantial metacognition, to various animals, who know much less and do much less, if any, metacognition, to nonconsc

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12

Dyson, Freeman. Spectral statistics of unitary ensembles. Edited by Gernot Akemann, Jinho Baik, and Philippe Di Francesco. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780198744191.013.4.

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This article focuses on the use of the orthogonal polynomial method for computing correlation functions, cluster functions, gap probability, Janossy density, and spacing distributions for the eigenvalues of matrix ensembles with unitary-invariant probability law. It first considers the classical families of orthogonal polynomials (Hermite, Laguerre, and Jacobi) and some corresponding unitary ensembles before discussing the statistical properties of N-tuples of real numbers. It then reviews the definitions of basic statistical quantities and demonstrates how their distributions can be made expl

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13

Hrushovski, Ehud, and François Loeser. The smooth case. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691161686.003.0012.

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This chapter examines the simplifications occurring in the proof of the main theorem in the smooth case. It begins by stating the theorem about the existence of an F-definable homotopy h : I × unit vector X → unit vector X and the properties for h. It then presents the proof, which depends on two lemmas. The first recaps the proof of Theorem 11.1.1, but on a Zariski dense open set V₀ only. The second uses smoothness to enable a stronger form of inflation, serving to move into V₀. The chapter also considers the birational character of the definable homotopy type in Remark 12.2.4 concerning a bi

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14

Hrushovski, Ehud, and François Loeser. Strongly stably dominated points. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691161686.003.0008.

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This chapter focuses on the properties of strongly stably dominated types over valued fields bases. In this setting, strong stability corresponds to a strong form of the Abhyankar property for valuations: the transcendence degrees of the extension coincide with those of the residue field extension. The chapter proves a Bertini type result and shows that the strongly stable points form a strict ind-definable subset Vsuperscript Number Sign of unit vector V. It then proves a rigidity statement for iso-definable Γ‎-internal subsets of maximal o-minimal dimension of unit vector V, namely that they

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15

Huybrechts, D. Fourier-Mukai Transforms in Algebraic Geometry. Oxford University Press, 2007. http://dx.doi.org/10.1093/acprof:oso/9780199296866.001.0001.

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This book provides a systematic exposition of the theory of Fourier-Mukai transforms from an algebro-geometric point of view. Assuming a basic knowledge of algebraic geometry, the key aspect of this book is the derived category of coherent sheaves on a smooth projective variety. The derived category is a subtle invariant of the isomorphism type of a variety, and its group of autoequivalences often shows a rich structure. As it turns out — and this feature is pursued throughout the book — the behaviour of the derived category is determined by the geometric properties of the canonical bundle of

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16

Baulieu, Laurent, John Iliopoulos, and Roland Sénéor. The Electromagnetic Field. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198788393.003.0003.

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The electromagnetic field. A brief review of Maxwell’s equations with a discussion of their invariance properties, both relativistic and gauge invariance. The formalism of Green’s functions is developed, including some physical applications.

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17

Segre, Beniamino. Some Properties of Differentiable Varieties and Transformations: With Special Reference to the Analytic and Algebraic Cases. Springer London, Limited, 2012.

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18

Segre, Beniamino. Some Properties of Differentiable Varieties and Transformations: With Special Reference to the Analytic and Algebraic Cases. Springer, 2011.

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19

Segre, Beniamino, and J. W. P. Hirschfeld. Some Properties of Differentiable Varieties and Transformations: With Special Reference to the Analytic and Algebraic Cases. Springer London, Limited, 2012.

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20

Baryakhtar, V. G., E. V. Zarotchentsev, and E. P. Troitskaya. Theory of Adiabatic Potential and Atomic Properties of Simple Metals. CRC, 1999.

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21

Akemann, Gernot, Jinho Baik, and Philippe Di Francesco, eds. The Oxford Handbook of Random Matrix Theory. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780198744191.001.0001.

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This handbook showcases the major aspects and modern applications of random matrix theory (RMT). It examines the mathematical properties and applications of random matrices and some of the reasons why RMT has been very successful and continues to enjoy great interest among physicists, mathematicians and other scientists. It also discusses methods of solving RMT, basic properties and fundamental objects in RMT, and different models and symmetry classes in RMT. Topics include the use of classical orthogonal polynomials (OP) and skew-OP to solve exactly RMT ensembles with unitary, and orthogonal

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22

Deruelle, Nathalie, and Jean-Philippe Uzan. Conservation laws. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198786399.003.0045.

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This chapter studies how the ‘spacetime symmetries’ can generate first integrals of the equations of motion which simplify their solution and also make it possible to define conserved quantities, or ‘charges’, characterizing the system. As already mentioned in the introduction to matter energy–momentum tensors in Chapter 3, the concepts of energy, momentum, and angular momentum are related to the invariance properties of the solutions of the equations of motion under spacetime translations or rotations. The chapter explores these in greater detail. It first turns to isometries and Killing vect

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23

Blackorby, Charles, and Walter Bossert. Interpersonal Comparisons of Well‐Being. Edited by Donald A. Wittman and Barry R. Weingast. Oxford University Press, 2009. http://dx.doi.org/10.1093/oxfordhb/9780199548477.003.0023.

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This article provides a short survey of the use of interpersonal comparisons in social evaluation. The focus of this discussion is on the principles for social evaluation that are welfarist, or those principles that use information about individual well-being to rank alternatives. The article reviews some of the most important characterization results for the welfarist social evaluation principles. A basic notation, along with a formal definition of social evaluation functionals, is introduced. The article then formulates some basic axioms for social evaluation orderings, and this is followed

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24

Swendsen, Robert H. An Introduction to Statistical Mechanics and Thermodynamics. Oxford University Press, 2019. http://dx.doi.org/10.1093/oso/9780198853237.001.0001.

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This is a textbook on statistical mechanics and thermodynamics. It begins with the molecular nature of matter and the fact that we want to describe systems containing many (1020) particles. The first part of the book derives the entropy of the classical ideal gas using only classical statistical mechanics and Boltzmann’s analysis of multiple systems. The properties of this entropy are then expressed as postulates of thermodynamics in the second part of the book. From these postulates, the structure of thermodynamics is developed. Special features are systematic methods for deriving thermodynam

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25

Louchet, Francois. Snow Avalanches. Oxford University Press, 2020. http://dx.doi.org/10.1093/oso/9780198866930.001.0001.

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This work is a critical update of the most recent and innovative developments of the avalanche science. It aims at re-founding it on clear scientific bases, from field observations and experiments up to strong mathematical and physical analysis and modeling. It points out snow peculiarities, regarding both static mechanical properties and flow dynamics, that may strongly differ from those of compact solids for the former, and of Newtonian fluids for the latter. It analyzes the general processes involved in avalanche release, in terms of brittle fracture and ductile plasticity, specific frictio

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26

Rings with Polynomial Identities and Finite Dimensional Representations of Algebras. American Mathematical Society, 2020.

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